Method and apparatus for acquiring and tracking a communications signal

ABSTRACT

A receiver is disclosed for acquiring and tracking a data signal in a highly stressed environment. The receiver comprises first and second I.F. sections, a mixer for translation from the first I.F. frequency to the second I.F. frequency, a 2 KHz bandpass filter at the second I.F. frequency, signal translator for synchronous translation of the signal at the second I.F. frequency to baseband, a digitizer for complex sampling operation on the baseband signal, a microprocessor for processing the digital samples, and a numerically controlled oscillator coupled to the mixer and controlled by the microprocessor. The microprocessor formulates matched digital discrete Fourier Transform filters which drive frequency, phase and symbol lock loops at the symbol rate. Each of the loop filters is formed by symbol-rate recursive, first-order equations. A novel mode control system is employed to implement an orderly transition through the receiver modes, comprising (i) out-of-band noise estimation, (ii) coarse frequency and time acquisition of the data signal employing a sequential probability ratio test and a handover process, (iii) frequency and symbol synchronization with the data signal, (iv) phase and symbol synchronization with the data signal, and (v) feedback loop lock confirmation. After loss of lock, the mode controller transfers the receiver operations back to the appropriate restart operation.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to data communication links operating in a highly stressed environment, and more particularly to receivers operable in such links.

2. Description of the Prior Art

Data communications links sometimes are required to operate reliably in highly stressed environments, such as, for example, space vehicles and deployable probes employed in planetary exploration missions, communications satellites and other space vehicles providing communications links to ground stations and the like. The link may be disturbed by such phenomena as amplitude and phase scintillation, atmospheric absorption, wind gusts and turbulence, probe or spacecraft gain, oscillator drift, Doppler effect, and Doppler rate and noise variations. Receivers utilized in such highly stressed environments may be required to acquire and track data signals impressed with these disturbances as soon as possible in order that data demodulation may then occur.

The present invention relates to receivers operable in such highly stressed environments. Because such receivers are utilized in space missions which are not only very expensive, but may take several years to complete from vehicle launch to mission completion, the performance and reliability requirements may be extremely rigid. State-of-the-art acquisition and demodulation techniques and receivers are understood not to be capable of meeting these rigid performance and reliability criteria in a fully satisfactory manner.

SUMMARY OF THE INVENTION

The present invention relates to a receiver adapted to operate in highly stressed environments to quickly acquire and track a signal to demodulate data carried by the signal.

Signal acquisition begins with an SPRT (sequential probability ratio test) search of the frequency uncertainty band. It is implemented by sweeping the band with a 4-point DFT (discrete Fourier transform) filter bank. Each filter is matched to the 512 Hz Manchester symbol rate which is twice the coded symbol rate 1/T=256 Hz, so that the bandwidth covered by the filter bank is 1536 Hz. Two filter sets separated by T/2 offset are formed at the Manchester symbol rate. At each dwell, the DFT filter outputs are accumulated and compared with the SPRT thresholds until it is decided that the signal is or is not present. After the signal is detected, the residual 1536 Hz frequency uncertainty is too large to permit FLL (frequency lock loop) startup so a handover procedure is initiated to narrow the uncertainty band to 512 Hz. In handover, multiple DFT filters are formed to cover the frequency and time uncertainty region. Outputs are accumulated and the filter with the largest sum is chosen. The chosen filter center frequency and time offset estimates the signal location if, in addition, the sum passes a Neyman-Pearson false alarm threshold test. Following handover, the FLL and symbol lock loop (SLL) are initiated. The FLL tracks the frequency and allows implementation of a least-squares estimate of the frequency and frequency rate. These estimates are calculated at the end of the FLL operation and are use to start the PLL (phase lock loop). The SLL tracks the symbol timing. When the PLL is turned on, its bandwidth is opened wide to improve acquisition and gradually narrowed to its operating value under the control of the PLL lock detector statistic. After lock is confirmed by the other lock detectors, the demodulator output data is considered to be valid and telemetry data is measured.

In the preferred embodiment, the receiver is implemented by a hybrid analog digital system. This partitioning allows the novel communication techniques to be implemented in the programmable digital processor, comprising a microprocessor system. After being hetero-dyned to I.F., the input signal is mixed with the NCO (numerically controlled oscillator) output, bandwidth limited by a BPF (bandpass filter), and synchronously translated to baseband where it is digitized with 8 bit resolution. The resulting inphase and quadrature digital data streams are processed to form a set of 4-point Discrete Fourier Transform (DFT) filters at the Manchester symbol rate 2/T=512 Hz. DFT outputs are used to form the tracking loop discriminants, lock detectors, and the symbol detection filter that provides the soft decision demodulator output.

A novel aspect of the receiver is that the FLL, PLL, SLL tracking loops operate at the symbol rate. FLL and PLL outputs drive the NCO and the SLL output drives the digital VCO. This VCO is a digital integrator whose output is a pointer that selects the start time for the DFT matched filters. Since the SLL is internal to the processor, the digitizer operates at 4 times the Nyquist rate of 2 kHz for the DFT filters. This enables the SLL to select the DFT timing at T/32 increments. Every T/2 seconds, the DFT filters are formed, and at T second intervals, the receiver state is updated. To improve the performance, the loop bandwidths for the FLL, SLL and PLL are opened wider at turn-on and then reduced with time.

While the overall receiver operation is disclosed, the present application is directed to novel techniques of signal acquisition, and frequency, phase and symbol timing synchronization. As described, the novel sequential probability ratio test is employed to determine a coarse estimate of the signal frequency, to within a 1536 Hz frequency uncertainty. The handover process then further narrows the frequency uncertainty region to within ±256 Hz, and determines the symbol timing to within ±T/16. The FLL implements two adaptive sets of FLL discriminant relationships, one used prior to AR and the second used after AR occurs. The PLL operates in a cycle slip mode and in a phase tracking mode. The novel FLL, PLL and SLL implementations allow simultaneous time control of the loop bandwidths and damping coefficients by the digital processor, adaptively adjusting the loop operations to actual signal conditions.

Other features and improvements and disclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

The above-mentioned and other features and objects of the present invention will become more apparent by reference to the following description, taken in conjunction with the followng drawings, where like reference numerals denote like elements, and in which:

FIG. 1 is a schematic illustration of the signal acquisition, tracking and demodulation as achieved in accordance with the preferred embodiment of the invention.

FIG. 2 is a block diagram illustrating the functions carried out by the preferred embodiment.

FIG. 3 is a functional block diagram of the receiver system of the preferred embodiment.

FIG. 4 is a simplified flow chart illustrative of the mode control system implemented in the preferred embodiment.

FIGS. 5a-5c are graphs illustrating the BPSK and Manchester symbols and the tracking filters in the time domain and the tracking filters in the frequency domain.

FIG. 6 is a graph illustrating the spectral and temporal locations of DFT filter energy accumulations employed in the sequential probability ratio test of the preferred embodiment.

FIG. 7 is a graph illustrating the spectral and temporal locations of DFT filter energy accumulations utilized in the SPRT handover operation of the preferred embodiment.

FIGS. 8a-8e are time chart illustrations of the relationship of true and estimated symbol timing to A/D complex samples and DFT filter operation.

FIG. 9 is a time chart illustrating the timing of operations in the frequency lock loop mode of the preferred embodiment.

FIG. 10 is a circuit model of the phase lock loop operating in the cycle-slip mode of the preferred embodiment.

FIG. 11 is a graph illustrating the spectral and temporal location of DFT filter accumulations of the preferred embodiment.

FIGS. 12a-12e are flow charts illustrative of the receiver mode control system of the preferred embodiment.

FIGS. 13a-13f are time domain charts illustrating the Manchester encoded BPSK data symbols and corresponding DFT tracking filters and transition detection filters.

FIG. 14 is a schematic block diagram illustrating a circuit model of the frequency lock loop of the preferred embodiment.

FIG. 15 is a schematic block diagram illustrating a circuit model of the symbol lock loop of the preferred embodiment.

FIG. 16 is a schematic block diagram illustrating a circuit model of the phase lock loop of the preferred embodiment.

FIG. 17 is a graph illustrating the Least Squares Estimation of the frequency and frequency rate which is provided to the PLL on initialization.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a communications receiver adapted for acquisition, tracking and demodulation of a data signal in a highly stressed environment. The following description is presented to enable any person skilled in the art to make and use the invention, and is provided in the context of a particular application and requirements. Various modifications to the preferred embodiment will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments. Thus, the present invention is not intended to be limited to the embodiment shown, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Table I illustrates exemplary disturbance phenomena which may exist in the highly stressed environments to which the preferred embodiment is adapted.

                  TABLE I                                                          ______________________________________                                         Disturbance        Magnitude                                                   ______________________________________                                         Amplitude Scintillation                                                                           0-3 db, .3 Hz Bw                                            Phase Scintillation                                                                               0-3 rad., .01 Hz Bw                                         Atmospheric Absorption (Cloud)                                                                    0-4 db                                                      Wind Gusts and Turbulence                                                                         ±8 Hz over 4 to 32 sec.                                  Spin of Orbiter Vehicle/Probe                                                                     7.5 radians/second                                          Oscillator Drift   110 ppm                                                     Doppler            ±35 kHz                                                  Doppler Rate       -10 Hz/Sec                                                  Noise Variation    0-1 db                                                      ______________________________________                                    

The environment described in connection with the preferred embodiment should be regarded as exemplary only; the novel features and principles of the invention have utility in other applications and operating environments.

The data signal received by the preferred embodiment is convolutionally encoded with an R=1/2, K=7 soft-decision convolutional data coding, and transmitted at 128 bits per second (bps), 256 symbols per second, using suppressed-carrier, binary phase-shifted-keyed (BPSK) modulation. Manchester symbol coding is added to the transmitted signal. As is well known, Manchester coding comprises the division of each BPSK symbol of length T into two Manchester bits each of length T/2, the first and second bits having opposed binary values to create an artificial signal transition from one binary value to the other in the middle of the BPSK symbol, to minimize symbol lock loop tracking problems. The Manchester coding does introduce an ambiguity into the receiver symbol timing, i.e., whether symbol timing is based on the actual symbol transitions or on the Manchester bit transitions. The receiver must therefore include an ambiguity resolution mechanism to ensure that the symbol timing loop is properly locked on the actual symbol transitions.

The overall signal acquisition operation of the receiver of the preferred embodiment is illustrated in FIG. 1. The frequency of the data signal is within a ±35 kHz uncertainty band, and a scan operation is first performed to narrow the uncertainty band in which the data signal is located to a band only 1536 Hz wide. As a result of a "handover" operation, the uncertainty band is further narrowed to a band ±256 Hz, and the symbol timing is determined to within ±T/16.

Using a frequency lock loop and symbol lock loop operation, the receiver further narrows the uncertainty band to one only ±17 Hz wide, resolves the symbol timing to within ±T/32, and determines the signal frequency rate of change to within ±1.7 Hz/seconds. At this point, the receiver operation shifts to a phase lock loop and symbol lock loop operation, and tracking and coherent demodulation of the data signal rapidly ensues.

This operation is accomplished in the preferred embodiment by a hybrid analog-digital implementation employing a microprocessor to perform digital filtering and processing functions. This receiver accomplishes the requirements for reliable rapid acquisition, reacquisition and tracking under severe link stresses and low C/No (signal power to noise power density ratio) operation and microprocessor computation limitations.

The simplified block diagram of FIG. 2 illustrates certain receiver functions implemented by the hybrid analog/digital structure, including the microprocessor. After being heterodyned to a first I.F. (intermediate frequency), the first I.F. signal 10 is mixed at mixer 20 with a numerically controlled oscillator (NCO) 15 signal for translation to a second I.F. frequency signal. The I.F. signal from mixer 20 is passed through bandpass filter 25 to digitizer 30. A local oscillator (LO) signal is also coupled to the digitizer 30 where it is used to quad mix the second I.F. signal to baseband prior to digitization. The digitizer 30 performs complex sampling (inphase I and quadrature Q baseband sampling), with 8 bit resolution.

Still referring to FIG. 2, the in-phase and quadrature digital data streams are fed to buffer 35, and then processed to form a set of 4-point Discrete Fourier Transform (DFT) filters at the Manchester symbol rate (2/T=512 Hz). The matched filter 40 drives both the symbol lock loop (SLL) and the frequency lock loop/phase lock loop (FLL/PLL). While these loops will be discussed in greater detail below, the SLL is a second-order loop which uses the buffer 35 to reduce the symbol timing error to within plus-or-minus T/32, where T is the symbol period. The FLL is a second-order loop which provides an estimate of the signal frequency.

The PLL tracks the phase of the baseband signal coherently. The FLL and PLL loops are closed through the feed-forward analog-to-digital (A/D) interface, and the feedback D/A interface via the numerically controlled oscillator (NCO).

In the SLL, the matched filter 40 is used to determine an SLL discriminant at discriminant 45. This discriminant is smoothed by second order loop filter 50, whose bandwidth decays linearly for the first 15 seconds during FLL operation and remains constant during PLL operation. The SLL output drives the digital voltage controlled oscillator (VCO). The VCO is a digital integrator whose output is a pointer which selects the start time for the DFT matched filter. The SLL is wholly internal to the microprocessor, with the digitizer 30 being operated at four times the Nyguist rate of 2 kHz for the IF filter 25 bandwidth. This enables the SLL to select the DFT timing at T/32 increments. Every T/2 seconds, the DFT filters are formed, and at T second intervals, the receiver state is updated. To improve the performance, the loop bandwidths for the FLL, PLL and SLL are opened wider at system turn-on and then reduced with time.

The FLL and PLL loops are also driven by matched filter 40. At discriminant 65, the microprocessor determines either a frequency (FLL) or phase (PLL) estimate discriminant which is smoothed by loop filter 70 and passed through amplifier 75 to form a loop output used to drive the numerically controlled oscillator (NCO) 15. The NCO output is fed to mixer 20, where it is mixed with the IF data signal to provide the second I.F. signal which is translated to baseband and digitized by digitizer 30.

It will be appreciated by those skilled in the art that the NCO output may be progressively swept through the frequency uncertainty band. The difference signal will be passed through filter 25, so that the 2 kHz frequency band through which the difference signal is to be passed may be correlated to a predetermined part of the uncertainty band.

Once the receiver has acquired and tracked the data signal, then the 8 bit matched filter 40 output is detected at detector 80 and the signal demodulated to provide a 3 bit data word.

Referring now to FIG. 3, a block diagram of the preferred embodiment of the receiver is illustrated.

The RF data signal 305 is input to the receiver at a frequency of approximately 1387 MHz. The signal is passed through a coupler 310 to bandpass filter 320. The purpose of bandpass filter 320 is to reject a signal which is sent to a redundant receiver (not shown), and to limit the bandwidth. The signal from filter 320 passes through amplifier 322 to mixer 325, where a mixing operation takes place with the output from frequency multiplier 384. The output of mixer 325 is a first IF frequency signal which is passed to IF filter 328. IF filter 328 covers the frequency range over which the receiver must search and find a signal, and provides sufficient additional range to allow the receiver to make out-of-band noise power estimates N to initiate the SPRT.

The output of the filter 328 is passed through amplifier 329 to mixer 330, the first-to-second I.F. frequency mixer. Mixer 330 centers the second I.F. signal in the 2 kHz tracking filter, by mixing the first I.F. signal with a combination of a fixed frequency from the reference oscillator and the NCO output signal.

The output of mixer 330 is fed to crystal bandpass filter 335. Filter 335 comprises the second IF tracking filter, a 2 kHz bandpass filter used to limit the bandwidth seen by digitizer 350 and to center on the signal. The output of filter 335 is passed through amplifier 337 to signal splitter 340. The output of splitter 340 is fed to mixers 342 and 344. Mixers 342 and 344, respectively, are mixed with signals from the 24 MHz oscillator 380 which has been passed through signal frequency divider 382. Splitter 340, mixers 342 and 344, and 90° phase shifter 346 perform a quad mixing which is an "I/Q" synchronous translation of the tracking filter bandwidth to baseband. This translation generates I (inphase) and Q (quadrature) signal components at baseband.

At baseband, the 2 kHz signal Z(t) has the complex representation Z(t)=I(t)+jQ(t), where Z(t) is the complex modulation function or envelope of the data signal from the tracking filter, which contains all the signal information. With this notation, I=Real (Z) and Q=Imaginary (Z).

The signal is centered at 1 kHz in alignment with the DFT tracking filters C2 and C4, described below. During phase-lock loop phase tracking, the signal is aligned with the I axis by the PLL.

Stable oscillator 380 provides the frequency and time reference signals from the receiver. The oscillator generates a 72.976659 mHz signal (for one receiver). It is passed through frequency multipliers 384 and 386, as well as frequency dividers 382 and 388.

Device 350 comprises the digitizer which receives quad mixing signals, and performs, sample-and-hold functions, multiplexer functions, and A/D conversion. In the preferred embodiment, the A/D converter is clocked at a sampling rate of 8192 Hz, four times the nominal bandwidth of filter 335. The A/D converter receives two baseband signals, the I and Q signals, and converts each signal to a serial binary data stream. The digital processor 360 comprises a microprocessor unit, and carries out programming and computing functions which are well known to those skilled in the art. The microprocessor design and implementation per se form no part of the present invention, and will not be described in further detail.

Numerically controlled oscillator (NCO) 365 is controlled by an output from a digital processor and converts the digital feedback signal from a digital tracking loop implemented in the microprocessor into a frequency which is proportional to the value of the digital feedback signal. This output in turn is mixed with a reference signal by mixer 367 and is provided through bandpass filters 370 and 372 to mixer 330.

The receiver signal flow will be readily apparent to those skilled in the art and, accordingly, need not be described in further detail.

A novel aspect of the receiver is that the SLL, FLL and PLL are driven at the symbol rate, 256 Hz, with digital matched filters in order to minimize microprocessor loading and to maximize performance. This is in contrast to the known prior art techniques which operate the loops at the Nyquist rate, 2 kHz, of the IF bandwidth seen by the loops. This prior art is summarized in the article "A Survey of Digital Phase-Locked Loops," by W. C. Lindsey and C. M. Ching, PROCEEDINGS OF THE IEEE, Vol. 69, No. 4, pp. 410-431, April 1981, and the IEEE Transactions on Communications, special issue on "Phase-Locked Loops," October 1982.

Another novel feature of the receiver is the implementation of the loop filters or integrators. Recognizing that the microprocessor software processing would enable ideal filtering, the first-order integration expressed in the Laplace domain as A/s is implemented in the time domain as the first-order recursive equation

    X(K+1)=X(K)+A*T*Y(K)                                       (1)

where X(K+1), X(K) are the loop outputs for symbols K, K+1, respectively, T is the symbol length, and Y(K) is the input for symbol K from the discriminant driving the loop. Second order integration is implemented as a concatenation of the Equation 1. This finite difference integration technique comprises the loop filter model.

This recursive equation, Equation 1, provides a "state space" formulation, with the "sampling" taking place at the "symbol rate" and not the IF bandwidth rate as assumed by known "Z-transform" theory. This result follows since the matched filters serve to effectively reduce the "Nyquist rate bandwidth" from the IF bandwidth to the symbol bandwidth which is identically equal to the symbol rate for matched filtering.

The net result of the use of this novel first-order recursive equation in the implementation of the loop filters is the minimization of the microprocessor computational loading, in contrast to previously known techniques.

Another novel aspect of the receiver is that the dependency of the loop discriminants on the input signal amplitude "A" has been minimized to achieve discrimination which approaches the ideal. The "ideal" discrimination occurs when the FLL, SLL and PLL are respectively driven by estimates of the frequency, timing and phase tracking errors which are essentially linear and independent of the signal input amplitude. To implement this aspect, each of the loop discriminants is normalized by the recursive estimate A of the signal amplitude A, i.e., the discriminant is divided by A or (A)², as appropriate for first or second-order loops.

The value of A is derived using the recursive equation

    A(K)=A(K-1)+α(|C2|-A(K-1))         (2)

where A(K), A(K-1) comprise the amplitude estimates at symbols "K" and "K-1", respectively, α is the inverse of the number of symbols whose amplitude is being averaged, and |C2| is the absolute value of the 4-point DFT filter C2 which tracks the signal and accumulates the energy at the "K-1" symbol.

This recursive equation has the advantages that (i) the value (|C2|-A(K-1)) is a relatively small number, thereby minimizing word size, (ii) A(K+1) is computationally stable with time and accuracy of word size, and (iii) the calculation is computationally simple. Tests have displayed a performance of the bit-error-rate (BER) vs. signal-energy-per-bit-to-noise-power-density-ratio (Eb/No) performance which is less than 1 db from the optimum ideal performance for BPSK modulated signals.

Another novel feature of the receiver is the use of a matched filter comprising a bank of complex discrete Fourier Transform (DFT) filters formed by "add-only" algebraic operations and located at the center of the bandpass filter spectrum after it has been synchronously translated to baseband.

The use of matched filters to maximize receiver signal-to-noise ratio is well known to those skilled in the art, and need not be described in detail here. Since the signal amplitude has been normalized, the matched filter need only match the phase rotations in the signal. As will be described in more detail below, these DFT filters are formed with computationally simple, "add-only" operations.

The "add-only" DFT filters comprise 4-point filters which spectrally cover the complete IF band-width seen by the loops and also minimize the burden of calculating the loop discriminants, normalization coefficients, lock detectors and other data. "Add-only" in this context means that only "add" and "90°" rotation calculations are needed to form the DFT filters, i.e., that there are no multipliers involved.

Still another novel feature of the receiver is that the timing loop, the SLL, exists completely within the digital domain (i.e., within the microprocessor) to keep it asynchronous, i.e., independent, from the A/D conversion. There is no loop timing feedback either through the NCO or A/D converter, thereby providing the freedom to move the time reference forward or backward within the microprocessor to achieve "optimal" loop performance. This also minimizes the microprocessor loading, since the SLL digital VCO and its output can be implemented as simply a counter whose output selects the "starting address" of the 4-point DFT filters. This requires that the A/D converter be run at some multiple K_(A/D) >1 of the Nyquist rate (8/T=2 kHz for the inphase and quadrature components of the preferred embodiment) to keep the timing filter and timing offset errors within tolerable limits. The value K_(A/D) =4 has been found to be adequate for the application of the preferred embodiment.

The above described novel features of the receiver allow it to accomplish the functions of signal acquisition, tracking and demodulation. A novel mode control system is implemented to control the operation of the receiver through its various modes of operation. The mode control system implements the orderly transition of receiver operation through five basic steps or modes: (1) out-of-band noise estimate; (2) coarse frequency and time acquisition, with a sequential probability ratio test (SPRT) and a handover algorithm; (3) frequency and symbol synchronization by the FLL and SLL; (4) phase and symbol synchronization by the PLL and SLL; and (5) lock confirmation and subsequent valid data demodulation.

The mode control system further implements an adaptive feedback procedure when loss-of-acquisition and/or loss-of-lock occurs. Each of the above modes and features will be described in more detail below, as will a detailed flow chart of the mode control system. To present an overview, FIG. 4 is a simplified flow chart illustrating the overall operational sequence of the receiver operations, as determined by the novel mode control system.

Referring now to FIG. 4, at step 105 the receiver is initialized, and at step 110 an estimate of the out-of-band noise energy is determined. The next step 115 is to perform the scan operation across the frequency uncertainty band using a sequential probability ratio test (SPRT), searching for the existence of signal. Step 120 is a decision point to decide if a signal was detected. If no signal was detected, then at step 125 a test is performed to determine whether five minutes has elapsed since calculating the out-of-band noise estimate. If not, the receiver operation reverts to the scan step 115 to scan the frequency uncertainty band again. If more than five minutes has elapsed, the receiver operation starts the initialization step 105 and determines another estimate of the out-of-band noise energy.

If at step 120 a signal has been detected, then at step 130 a "handover" operation occurs, wherein the receiver commences the transition from the SPRT scan to the FLL and SLL operation. At step 135, "FLL/SLL pull-in," the FLL and SLL start up, with loop parameters which decay from initial start-up values to parameters chosen for steady-state operation.

At step 145, values for the frequency f and frequency rate f are estimated, using a least-squares estimation process. At step 150 a decision is made to determine whether the ambiguity has been resolved as to whether the SLL has locked onto the symbol or the Manchester bit transitions. If ambiquity resolution (AR) has been accomplished, then at step 155 a timer is checked to determine if the elapsed interval since commencing the estimation process at step 140 is longer than 18 seconds. If AR has not yet occurred, then at step 160 a timer is checked to determine if the elapsed interval since entering step 150 loop is longer than 18 seconds, and if not, the receiver operation back to step 145 to determine new f and f estimates. If the timer at step 160 indicates an elapsed interval longer than 18 seconds, the program control shifts the operation back to decision point 125, to determine whether to commence a new scan of the uncertainty band with a new out-of-band energy estimate.

At step 155, if the elapsed interval since entering step 145 is longer than 18 seconds, then commencing at step 165, the receiver operation mode shifts to the phase and symbol synchronization mode. At step 170, a decision is performed to determine whether the PLL is in lock. If not, then at step 180, a timer is checked to determine whether the elapsed time interval since the out-of-lock condition commenced is longer than 8 seconds, and if not, the operation shifts back to repeat step 165. If the elapsed interval is greater than 8 seconds, then mode control shifts the receiver operation back to the SPRT handover operation at step 130.

At step 170, if the receiver is in phase lock, then the receiver is ready to commence valid data demodulation at step 175. All lock detectors, i.e., for the FLL, SLL and PLL, are periodically checked at step 185 to ascertain whether the receiver is still locked onto the signal. If not, then interval timers at decision points 190 and 195 determine, based upon the length of time the out-of-lock condition has persisted, whether receiver operation reverts back to step 165 (the PLL), step 130 (the FLL), or to step 105 (initialization).

The above simplified flow chart of FIG. 4 is illustrative of the overall receiver operations, which has been adapted to the particular application of the preferred embodiment. The flow chart does exemplify the powerful signal acquisition, tracking and demodulaiton system and operation of the receiver. With this background, the receiver operation and its mode control system will be discussed in detail.

Out-of-Band Noise Power Estimate

The noise power estimate N is initialized by an 8 second out-of-band noncoherent energy accumulation. Four second accumulations are done at frequencies 1536 Hz beyond each end of the uncertainty band. The initial noise power estimate is performed at frequencies outside the uncertainty band because it is certain that these frequencies will be uncontaminated by the presence of the signal. As indicated in FIG. 4, this estimate is reinitialized at 5 minute intervals until a signal has been detected. The out-of-band noise power estimate N is determined using the first order recursive formulation of Equation 3 described below.

Scan Mode

The receiver signal acquisition or scan mode utilizes a sequential-probability-ratio test (SPRT) in a novel implementation to rapidly detect the approximate location of the signal in frequency and time.

The implementation comprises the modification of the known single filter detection SPRT test to allow the simultaneous use of the multiple 4-point DFT filters which cover the I.F. filter bandwidth, to result in a multiple add-only detection filter SPRT. This improved SPRT has several significant performance improvements, including faster signal search and acquisition, a higher signal-to-noise power ratio (SNR) in each SPRT detection filter which results in less sensitivity to C/N_(o) fluctuations and hardware induced gain changes across the frequency search band, and continuous noise power updates to minimize the impact of noise power variations with time and/or test.

As described above, the novel SPRT of the preferred embodiment is preceeded by the determination of the out-of-band noise power estimate N, made by accumulating the energy in 4-point DFT filters C1, C2, C3 illustrated in FIG. 5, using the one-step recursive equation

    N(K)=N(K-1)+α(|C|.sup.2 -N(K-1)    (3)

where |C| is the magnitude of energy accumulated in DFT filters C1, C2, C3 at step K-1, and α is the inverse of the number of symbols being averaged over the preceding eight seconds, i.e., 1/2¹² =1/2048.

After each unsuccessful sweep across the frequency uncertainty band, the noise estimate is updated by the noise power in each 1536 Hz wide windows across the uncertainty band. If the signal was found during the sweep, the previous estimate is not updated. The update is calculated by energy accumulations in a recursive filter with an 8 second time constant. The noise power in each window is an unbiased power, i.e., it does not have the SPRT bias subtracted off.

In a broad sense, this SPRT consists of stepping the 2 kHz I.F. bandwidth through the frequency uncertainty band in 1536 Hz windows. At each window, six 4-point DFT SPRT tests are simultaneously performed to determine if the signal is present within the 1536 Hz window, which is the spectral width of the DFT filters C1, C2, C3 used in the test, as illustrated in FIG. 5. These six DFT SPRT filters are C1, C2, C3 at 0 and T/4 time offsts. These energy accumulations are tested against an upper threshold (signal) and a lower threshold (noise) every eight bit-times until a decision for either signal or noise is reached, or a two second timeout is reached whereupon it is decided noise is present.

If no signal is detected, the I.F. band is moved over 1536 Hz to the next window, and dwells there until it is determined that a signal is or is not present. The test continues in this manner until the entire frequency uncertainty region has been searched, the out-of-band noise power estimate is updated and the next SPRT sweep started.

The sweeping of the uncertainty band is implemented by controlling the numerically controlled oscillator (NCO) frequency so that any difference signal formed from mixing the IF signal and NCO signal, and synchronously translated to baseband would be within the frequency windows subtended by DFT filters C0, C1, C2 and C3 commencing at baseband and extending to 2 kHz.

When a signal is declared present, the frequency address, the signal level, and the time to pass the signal threshold are stored. The window with the shortest time to pass the signal threshold is declared the best estimate of the signal frequency. If two windows have the same time to pass the signal threshold, the winner is the window with the highest energy. All windows in the uncertainty band are tested before a final decision is made.

The tracking and detection filters are illustrated in FIGS. 5a-5c. As shown in FIG. 5a, in the time domain, each BPSK symbol has a period T, and comprises two Manchester bits, each of period T/2. The attenuation charcteristic of the I.F. tracking filter is illustrated as an ideal filter in the frequency domain in FIG. 5a; the filter has bandwidth of 2 kHz.

FIG. 5b illustrates, in the time domain, the encoded Manchester symbol, and the attenuation characteristics of the four 4-point DFT filters C0, C1, C2, C3, which cover the 2 kHz IF filter bandwidth. The C2 tracking filter is shown centered at 1 kHz and is matched to the Manchester bits. Th notation C2(1) refers to the C2 filter aligned on the first Manchester bit, and C2(2) refers to the C2 filter aligned on the second Manchester bit.

Digital filtering is well known to those skilled in the art, as are DFT digital filters. The terminology "4-point," in the context of digital DFT filters, refers to the number of complex samples per symbol which are accumulated in the DFT integrators or registers to determine the energy detected within the DFT bandwidth. Thus, for a 4-point DFT filter, four samples from the A/D converter will be integrated or added over a symbol to form the value for the signal and noise energy in the filter bandwidth.

The four DFT filters C0, C1, C2, C3 each have a 512 Hz bandwidth, centered respectively at 0, 512, 1024 and 1536 Hz. The nominal bandwidth of each ideal 4-point filter is determined by the Nyquist sampling rate. Each of the filters has 4-points or samples, each separated in time by (1/2056)=(T/8) seconds. From a Nyquist sampling rate viewpoint then, the noise bandwidth of each 4-point filter is the inverse of this symbol Manchester bit length, i.e., 2/T=512 Hz.

Since the center frequencies of the four filters are separated in frequency to cover four windows in the 2 kHz IF tracking filter, the matched filter processing must phase rotate the samples or points to allow the samples to be coherently added. The filters are matched to the signal, and rotating in the opposite direction and at the same rate as the signal.

The C0filter is centered at 0 Hz and, therefore, the inphase I and quadrature Q samples may be directly summed without phase rotation. To avoid picking up any d.c. energy, however, the C0filter integration is not used.

Filter C1 is centered at 512 Hz, i.e., the first harmonic, which rotates through 360° for each Manchester bit symbol with respect to the fundamental. Hence, since the four points are equally spaced in time, each point should be rotated by successive -90° phase increments, i.e., -90°, -180°, -270°, -360°. A -90° rotation of the complex sample (I+jQ) consists of multiplying the sample by (-j). Hence, the result is (-j)(I+jQ) or (+Q-jI). This is a very simple operation for the microprocessor; it need only interchange the values in the I and Q buffers, and invert the Q value. The second point is rotated by -180°, which consists of multiplying the complex sample (I+jQ) by -1, i.e., (-1)(I+JQ)=(-I-jQ). This is also a very simple operation, simply inverting the I and Q values to be entered in the respective buffer.

The third point of the C1 filter is rotated through -270°, which consists of multiplying the complex sample (I+jQ) by (+j), i.e., (+j)(I+jQ)=(-Q+jI). Again, this is a computationally simple operation. The fourth point is rotated by -360°, which amounts to multiplication of the sample by +1, i.e., no change in the sample.

The C2 filter is aligned on the second harmonic at 1024 Hz. This filter must rotate through two complete rotations in one symbol so that each point is successively phase rotated -180°, -360°, -540° (i.e., -180°) and -720°, respectively.

The C3 filter is aligned with the third harmonic at 1536 Hz and rotates through three complete cycles for each symbol. Hence, each point must be successively rotated through -270° phase rotations, -270°, -540°, -810° (i.e., -90°) and -1080°, respectively.

The DFT filters described above are implemented with add-only functions.

Now referring to FIG. 5c, tracking/detection filter C4 is formed by C2(1)-C2(2), to comprise an 8-point DFT which is matched to the BPSK symbol. The effective attenuation characteristic of this filter is illustrated in the frequency domain in FIG. 5c, centered at 1 kHz. This 8-point DFT filter has an effective noise bandwidth of 2 kHz/8, i.e., 256 Hz.

After each sweep is completed through the 2 kHz I.F. band, the SPRT determines whether or not a signal is detected. This SPRT determination comprises four basic steps.

The first step is to accumulate the energy ψ in each of six DFT filters C1, C2, C3 at 0 and T/4 offsets; the six energy accumulations are ψ₁ -ψ₆. This is illustrated graphically in FIG. 6, which comprises a plot of time versus frequency, with the individual filters C1, C2, C3 indicated at times 0 and T/4. The energy ψ is accumulated using the equation ##EQU1## where the index K indicates a summation over consecutive Manchester bits K, K+1, . . . ,

    β=1+α.sub.o /2.

|C|=energy in DFT filters C1, C2, C3 at step K-1,

α_(o) =Design point SNR for the DFT filters,

approximately the lowest SNR expected to be detected.

If a signal is present having a SNR>α_(o) /2, the energy value ψ will increase with K and eventually exceed a positive or upper threshold value λ_(B) N. If no signal is present, the ψ will decrease with K and quickly fall below a negative or lower threshold value λ_(A) N. The second step of the test follows from these characteristics and comprises the SPRT detection rule

    -λ.sub.A N<ψ<λ.sub.B N.                  (5)

If ψ is greater than -λ_(A) N, but less than λ_(B) N, the result is that no decision is made so the SPRT is continued. If ψ is greater than λ_(B) N, the decision is made that a signal is present. If ψ is less than -λ_(A) N, the decision is made that only noise is present. If the test continues for more than two seconds without a decision, a default decision is made that there is no signal. A decision is required as to the energy values ψ₁ -ψ₆ from all six DFT filters before the dwell is terminated.

If a signal has been detected in more than one energy value ψ₁ -ψ₆, then the DFT filter with the shortest-time-to-pass the threshold is selected unless there is a tie whereupon the largest ψ value is selected.

The third step of the SPRT is that the energy values ψ are continuously used to update the noise power estimate N using the recursive equation

    N(K)=N(K-1)+α(ψ(K-1)-N(K-1))                     (6)

where the ψ now has the bias term βN deleted. The correction to the noise power estimate is applied at the end of each sweep if the signal has not been found.

The fourth step to the SPRT is that the DFT locations are dithered by T/8 in time and 1/T=256 Hz in frequency at the end of each sweep to improve the detection performance with respect to a signal that may have fallen into a "time and frequency dip" between the DFT filters. If the signal was not found, and if no new noise estimate is requested and if the elapsed time searching has not exceeded 10 minutes, another sweep is begun. The new sweep will have a dither of T/8 in timing and 256 Hz in frequency to maximize the probability of locating the signal if it was missed the previous sweep. If the signal is missed again, the next sweep will have a zero-time and zero-frequency dither (from the original non-dithered frequency and time).

Handover from SPRT to FLL/SLL

Once the decision is made that a signal has been detected, then the receiver is placed in a novel "handover" mode used to implement the mode transition from the SPRT mode to the FLL/SLL mode. SPRT signal location accuracy is ±768 Hz corresponding to the 1536 Hz search window. This wide frequency uncertainty is caused by the noise contamination of the energy statistics ψ₁ -ψ₆ so that a more accurate frequency decision cannot be reliably made. Also, this is the reason a reliable timing decision cannot be made. This handover mode is required to reduce the SPRT frequency Δf and time Δt uncertainties in the signal location to the point where acquisition by the FLL and SLL can occur. The handover mode also serves to verify that the signal has indeed been found by the SPRT before proceeding to the FLL/SLL mode. This novel handover mode comprises two steps, an estimate of the signal location, and verification that the signal is present at that location.

The novel process of locating the signal is an extension of known maximum likelihood estimation (MLE) techniques. With the known techniques, the frequency Δf and time Δt location of the signal detected at Δf=Δt=0 by the SPRT is estimated by constructing multiple sets of signal position hypotheses throughout the Δf, Δt region, and then selecting the best hypothesis in the maximum likelihood sense. Each hypothesis is the energy ψ of a 4-point DFT accumulated over a dwell period. The optimum hypothesis using this known technique is the largest of the energy ψ values. This technique is inadequate because of poor detection probability and false alarm performance. The following novel detection technique overcomes these disadvantages.

The distribution of DFT filter energy accumulations ψ is illustrated in FIG. 7. Each "X" indicates an energy accumulation for a particular time and frequency location. Twenty-four accumulations are indicated, including those centered at 768 Hz and 1280 Hz, which are obtained in the preferred embodiment by "notching" the local oscillator frequency. The signal location estimated by the SPRT is at T=0, f=1024 Hz.

The signal location decision rule is defined using the following notation:

ψ(k,i)=Accumulated DFT energy over 512 Manchester bits (1 second) at position Δf=(256·k)Hz, Δt=(i-1)T/8 relative to the position Δf=Δt=0 of the SPRT signal location estimate.

Δf, Δt=Frequency, time position in the coordinate frame associated with the ψ distribution in FIG. 7.

The signal location decision rule comprises the following steps:

Step 1: Reduce the search region to 3 continguous frequencies by finding the largest triplet of contiguous energy values ##EQU2##

Step 2: Find the largest pair of contiguous energy values within the reduced Step 1 region (3×4=12 hypotheses) ##EQU3##

Step 3: The estimated signal location time Δt is the position of the largest pair in Step 2.

    Δt=(i-1)T/8

Step 4: The estimated signal location frequency Δf is the position of the largest ψ within the largest pair in Step 2. ##EQU4##

In other words, for each row of FIG. 7 each of the four contiguous triplets is examined to find the maximum sum resulting in three contiguous columns from which the signal location can be found. For each of the four rows of these three columns, there will be three terms which are candidates for the signal. Of these three terms, the pair whose sum is greatest is found. The row with the maximum pair will be the estimate of timing. The maximum single term of the maximum pair will be the selected frequency estimate of the signal.

The second aspect of the handover mode is signal verification. This verification step utilizes a Neyman-Pearson (NP) test to prevent signal false alarms from activating the FLL/SLL mode, rather than increasing the SPRT acquisition time to reduce the false alarm rate or probability P_(F). The NP test occurs after completion of the signal location step in the SPRT handover mode.

The NP test compares the accumulated energy test statistic ψ(k,i) from the signal location algorithm, with a threshold equal to λN, where N is the noise power estimate from the SPRT. The following notation is used for the definition of the signal verification test:

N=Noise power estimate from out-of-band noise measurements prior to and during the SPRT

λ=NP threshold constant of proportionality

=False alarm threshold constant

λN=NP threshold

ψ(k,i)=Accumulated DFT energy over 1 second total dwell at the estimated signal location k,i in FIG. 7.

The handover signal verification comprises the following:

    ψ(k,i)>λN                                       (7)

If ψ(k,i) is greater than λN, then the test result indicates that a signal is present. If ψ(k,i) is less than λN, then the test result is that only noise is present (no signal).

The false alarm threshold constant λ is determined using the assumptions that the NP detection threshold equals λN, ψ is the energy sum over a one second interval, and N is the noise estimate over a two second interval. The performance parameters are P_(D) =Prob(ψ|H1≧λN), where P_(D) is the probability of a signal passing the NP test, i.e., the probability of passing the test when a signal is present corresponding to hypothesis H1, and P_(F=) Prob(ψ|H0≧λN), where P_(F) is the probability of a false alarm, i.e., the probability of ψ passing the test when only noise is present corresponding to hypothesis H0. The threshold constant λ is set at the C/N_(o) design point for the desired P_(D), P_(F) performance. The result is that λ has been calculated to be 1.21 for P_(D) =0.99999 and P_(F) =0.00003.

As a result of the SPRT handover, the signal location is determined to within ±256 Hz and ±T/16 seconds. This signal location is provided to commence operation of the FLL/SLL.

Frequency Lock Loop (FLL)/Symbol Lock Loop (SLL)

The FLL and SLL loops include several novel features to provide rapid acquisition performance over a relatively wide frequency offset Δf and time offset Δt pull-in range. These features include the DFT frequency discriminant for the FLL, FLL time-dependent parameter control law relationships, the SLL discriminant, and the SLL time-dependent parameter control law.

The two FLL modes are the acquisition and track modes. In the preferred embodiment, acquisition starts at completion of the SPRT handover and lasts for six seconds. The SPRT handover frequency Δf and timing Δt errors respectively are tracked out by the FLL and SLL simultaneously during their acquistion phases. The track mode parameters are constant for the FLL and SLL. In addition to the (time dependent) control law change between modes, the completion of ambiguity resolution (AR) marks a change in the frequency disciminant from a Manchester bit to a full symbol as well as the replacement of the acquisition discriminant by the tracking formulation.

The FLL loop is a second-order loop modelled by the equivalent circuit shown in FIG. 14. The I.F. signal f is provided to mixer 334a, where it is mixed with the signal f from NCO 365a. Mixer 334a and NCO 365a correspond respectively to mixer 334 and NCO 365 shown in the block diagram of FIG. 3. The output of the mixer 334a is a signal having frequency Δf. The discriminant Δf produced by estimator 363a and the loop filter 364a having the Laplace transform characteristic (G/S)(1+(A/S)) are implemented within the microprocessor of the receiver. The output of the loop filter is X, which is provided as the digital control signal to the NCO.

The operation of frequency or phase lock loops is well known in the art, and need not be descibed in detail here. The loop coefficients G and A are adaptively determined by the microprocessor, as will be described below. The following relationships are the one-step recursive equations used to calculate the FLL loop filtering for each symbol input Δf from the FLL discriminant.

Loop Filtering:

G A/s² :

    X1=X1+G·A·T·Δf

    X2=X2+T·X1

G/s:

    X3=X3+T·Δf

NCO Input:

    X=X3+X2

where "T" represents the symbol length. For loop initialization, the integration constants are the initial values for X1, X2, X3 which are set equal to

X1=0

X2=0

X3=Handover frequency estimate where an equivalent choice is to set X3=0 and X2=handover frequency estimate.

The FLL loop is driven by the output Δf of the frequency discriminant whose function is to derive the estimate Δf of the actual frequency error Δf seen by the FLL. In the preferred embodiment, a frequency discriminant Δf with the following basic characteristics is desired:

A. Acquisition and Track Prior to Ambiguity Resolution:

1. Linearity E(Δf)=ηΔf: Modest Δf

2. Data insensitive

3. Capability to operate with Δt=±3T/32 timing offsets

4. Pull-in range to +/- 384 Hz

5. Graceful degradation with low C/N_(o)

6. Discrimination over Manchester bit.

B. Track after Ambiguity Resolution:

1. Linearity E(Δf)=ηΔf: Modest Δf

2. Data insensitive

3. Tracking range to +/- 192 Hz

4. Discrimination over symbol

These desired characteristics assume that the Δf jitter does not degrade with decreasing C/N_(o) faster than a square-law effect.

With these basic characteristics, the following relationships determine the FLL frequency discriminant Δf.

A. Acquisition and Track Prior to AR: ##EQU5## where C_(N),C_(N) =4-Point DFT tracking filter N=1, 2, 3 over Manchester bit K, with C_(N) =Complex conjugate of C_(N) ##EQU6## B. Track after AR: ##EQU7##

    E(Δf)=ηΔf for modest Δf.

Thus, the Δf prior to ambiguity resolution (AR) is the new DFT discriminant, and the Δf after AR is a novel modification to the known IQ discriminant, comprising the normalization of the IQ discriminant by <|C₂ |>².

The signal amplitude estimate A=<|C₂ |>_(K) is equal to the one-step recursive average of the DFT filter C₂ given by Equation 11.

    <|C.sub.2 |>.sub.K =<|C.sub.2 |>.sub.K-1 -α(|C.sub.2 |.sub.K-1 -<|C.sub.2 |>.sub.K-1),                 (11)

where |C₂ |_(K-1) is the absolute value measurement of C₂ for the Manchester bit K=1.

This amplitude normalization is used throughout for the loop discriminants and lock detectors.

A second novel feature of the FLL/SLL mode is the FLL parameter control law. For the preferred embodiment, a number of parameter guidelines are observed. During signal acquisition, these guidelines include the following. The FLL loop damping coefficient ξ is selected to accomplish step response goals of achieving of a short first-zero-crossing-time, and low overshoot. For these guidelines, the allowable range in loop damping coefficient ξ values is from 0.707 to 3. With respect to B_(L), the one-sided loop noise bandwidth, since the loop jitter is proportional to the square root of B_(L), the loop natural frequency is proportional to B_(L), and the first-zero-crossing-time is proportional to 1/B_(L) ; this results in an allowable range in B_(L) of 0.5 to 1.5 Hz.

An additional set of acquisition guidelines, specifically referring to the functional form of the acquisition control law are the following. The frequency offset due to the loop stresses caused by changes in frequency with respect to time (df/dt) is proportional to (dG/dt/G² A), where G is the loop gain. To have a constant damping coefficient ξ, analysis indicates the B_(L) change with time t should be proportional to 1/√t.

Tracking guidelines used to select the values for ξ, B_(L) are the following. It is desired that the damping coefficient ξ=0.707. Since the loop jitter is proportional to the square root of B_(L) and the independent-sample rate to drive the f and df/dt estimator is approximately equal to 2 B_(L). This restricts the allowable B_(L) range from 0.1 to 1.0 Hz.

With these guidelines, the control law relationships of Equations 12, 13 and 14 determine the FLL operation. ##EQU8##

Both the bandwidth B_(L) and damping factor ξ follow the generalized equation 12 for X. Based upon the foregoing relationships, the initial loop parameters for X=X_(o) are B_(L) =1.12 Hz, ξ=2.0, η=0.62 (constant), G=6.801 and A=0.264. The final loop parameters, for X=X₁, are B_(L) =0.28 Hz for t₁ =6 seconds, ξ=0.707 for t₁ =2 seconds, G=1.204 and A=0.373.

A novel feature of this loop control law is that during FLL mode operation, both the noise bandwidth and damping coefficient which specify the loop parameters G, A may be simultaneously time controlled by the microprocessor. This provides greatly increased adaptive FLL performance.

During FLL operation, the symbol lock loop (SLL) is driven by the estimate Δt of the SLL timing error Δt provided by the SLL loop discriminator.

The second order symbol lock loop is modelled by the circuit shown in FIG. 16. The bit or symbol transition time t of the received BPSK waveform is provided to "mixer" 420, where it is "mixed" with a time estimate t, which is the SLL estimate of t. t controls a pointer that determines the start time for the tracking/detection 8-point filter C4 summation, as well as the start time for the other 4-point DFT filter summations. The timing offset Δt=(t-t) is provided to estimator 405 where the timing discriminant Δt is determined. The discriminant is filtered by a loop filter having the Laplace transform characteristics G(1+A/s). The output of filter 410 is digital signal X, which controls digital NCO 415, which has the Laplace transform characteristic 1/s. The digital NCO output is t. This SLL is implemented entirely within the receiver digital processor.

The following relationships comprise the one-step recursive equations used to calculate the loop filtering plus the digital NCO output for each symbol, from the SLL discriminant output Δt.

Loop filtering GA/s: X1=X1+G·A·T·Δt

Digital NCO input: X=G·Δt+X1

Digital NCO output G/s: t=t+G·t·X

For loop initialization, the integration constants are the initial values for X1, t set equal to X1=0, t=handover timing estimate. The loop coefficients or parameters G, A are calculated for each symbol, as described below. During FLL operation, phase coherency between contiguous symbols is not required for any of the functions, so the SLL loop is closed with the timing quantization or granularity equal to T/32, the A/D digitization interval. During PLL operation, this will be changed, as described below.

As previously descrived, the SLL is internal to the microprocessor. For the preferred embodiment, the timing discriminant Δt has the following basic characteristics:

Acquisition and Track prior to AR:

1. Linearity E(Δt)=ηΔt, for modest Δt values

2. Operable with all data transition densities

3. Operable with Δf=+/- 256 Hz frequency offsets

4. Pull-in range over all Δt

5. Stable lock points at mid-bit and bit transitioning

6. Graceful degradation at low C/N_(o)

7. Discrimination over Manchester bit

Acquisition and Track after AR:

1. Linearity E(Δt)=ηΔt: Modest Δt

2. Data insensitive

3. Operable with Δf=+/- 192 Hz frequency offsets

4. Tracking range over all Δt

5. Stable lock point at mid-bit transitioning

6. Graceful degradation at low C/N_(o)

7. Discrimination over symbol

These characteristics assume that the Δt does not degrade with C/N_(o) at a rate faster than the square-law effect.

The symbol timing loop operation is graphically illustrated in FIGS. 8a-8e. FIG. 8a illustrates the true symbol location, which starts at time t and the SLL estimate of the symbol location, starting at t. The symbols depicted are Manchester bit symbols. Δt comprises the difference between t and t, Δt=t-t. The A/D converter complex samples are illustrated as points along the time axis in FIGS. 8a-8e.

The samples for tracking filter C2 are depicted in FIG. 8b. Filter C2 comprises C2(1), a 4-point DFT filter matched to the first bit of the Manchester symbol, and C2(2), a 4-point DFT filter matched to the second bit of the Manchester symbol. In FIG. 8b, the samples for C2(1) are depicted as "1" occurring every fourth A/D sample in the first symbol, and the samples for C2(2) are illustrated a "2" occurring every fourth sample in the second Manchester bit. As described above, in the preferred embodiment the A/D converter is driven at 4 times the Nyquist symbol rate. However, only every fourth sample is utilized to form the DFT filters.

As described above, tracking/detection filter C4 is an 8-point un-normalized DFT filter formed by subtracting C2(2) from C2(1), C4=C2(1)-C2(2).

The SLL discriminant has the form of a "bang-bang" function, and is calculated from the output of matched filters with differing time-alignment. Prior to ambiguity being resolved, the matched filters are formed from 3 complex data points, and are calculated across a nominal bit timing and across the mid-bit transition, a T/2 offset. After ambiguity is resolved, 4 complex points are used to form the filters, and the matched filters are calculated only across the mid-symbol transition. The SLL discriminant is normalized by the estimate of the magnitude of signal-plus-noise energy in DFT filter C2, <|C₂ |>.

The 3-point un-normalized DFT filters formed to calculate the SLL discriminant Δt prior to AR are depicted in FIGS. 8c and 8d. The DFT filters calculated across the mid-bit transition are depicted in FIG. 8c as C₊ (1), C-(1), with the three A/D samples for C₊ (1) depicted as "+," and the three samples for C₋ (1) depicted as "-." The DFT filters calculated across the bit transition are depicted in FIG. 8d as C₊ (2) and C₋ (2), with the three A/D samples for C₊ (2) depicted as "+," and the A/D sample for C₋ (2) depicted as "-" (the other two samples for C₋ (2) are in the next bit, not shown in FIG. 8d).

The 3-point DFT filters are used prior to AR instead of 4-point filters. Although the 3-point filters have more noise due to their wider noise bandwidth (682 Hz), they are less susceptible to errors caused by excessive timing jitter than the 4-point filters. The 3-point filters are centered at the same frequency 1024 Hz as the 4-point filter C₂, and the same phase rotation, 720°, is applied.

The SLL discriminant Δt used in SLL operation prior to ambiguity resolution is calculated in accordance with Equation 16. ##EQU9##

After ambiguity resolution occurs, the SLL discriminant is calculated from the output of a 4-point DFT across the mid-bit, i.e., Manchester transition. The 4-point DFT is used because it provides a higher signal-to-noise ratio (SNR). The two 4-point unnormalized DFT filters are depicted in FIG. 8e as C₊, C₋, with the A/D samples depicted as "+" and "-," respectively. The SLL discriminant Δt used after ambiguity resolution is calculated in accordance with Equation 17. ##EQU10##

A discriminant gain or scale factor η is used to ensure a 1:1 relationship between the SLL input and output. For modest Δt values, E(Δt)=ηΔt, resulting in a selected value for η=0.4, for the design point C/N_(o) =25 db-Hz and 62.5% data transitioning. Other design points and applications would, of course, result in different scale factor values.

The SLL damping factor ξ and bandwidth B_(L) parameters are developed using the following guidelines. For the preferred embodiment, it was desired that the damping factor ξ be between 0.707 and 2.0. The loop jitter σ.sub.Δt is proportional to √B_(L), the loop first-zero-crossing time is proportional to 1/B_(L), and the loop offset due to timing drift is proportional to 1/B_(L) ². It was desired that the loop jitter be less than or equal to T/32, and that the first-zero-crossing time be less than or equal to six seconds for acquisition and twenty seconds for tracking. The offset due to timing drift was desired to be much less than T/32.

With these guidelines, novel control law relationships were developed to allow the simultaneous time control of both B_(L) and ξ. In the preferred embodiment, the damping coefficient ξ is 1.0. The bandwidth B_(L) follows the relationship of Equations 18.1 and 18.2.

    B.sub.L =0.5-(0.5-0.15)(t/15) Hz,                          (18.1)

for t≦15 seconds

    B.sub.L =0.15 Hz,                                          (18.2)

for t>15 seconds

The SLL parameters G and A are calculated from B_(L) and using the relationships described in Equations 19 and 20: ##EQU11##

For the values η=0.4 and ξ=1, G=8 B_(L) and A=0.8 B_(L). Thus, by adaptive control of B_(L) by the microprocessor, simultaneous time control of the SLL loop parameters G and A can be achieved.

The discriminant Δt, then, is smoothed with a second order filter. The filter bandwidth B_(L) decays linearly for the first 15 seconds during the FLL mode. The two loop parameters (G and A) are updated once per second such that the bandwidth B_(L) decays from 0.5 Hz to 0.15 Hz, while the filter damping factor remains at a constant value of 1.0 at all times. (When the SLL is operating during PLL, the bandwidth and damping have the constant values of (0.15 Hz) and (1.0), respectively.)

The SLL filter output is used to provide a new read-out pointer controlling the buffer. The result of the ambiguity resolver processing is an output which causes the pointer to remain the same (if the assumed timing was found to be the symbol transition) or to be increased by T/2 (if the assumed timing was found to be the mid-symbol transition). This AR correction is calculated only once during the FLL mode, and is not recalculated until the FLL mode is restarted.

Least-Square-Estimation

The use of an NCO-input-driven, least-squares-estimate (LSE) of the frequency f and frequency rate df/dt being tracked by the FLL represents a novel technique which significantly enhances the FLL performance. LSE estimates f, df/dt of the f, df/dt are derived from the FLL loop filter input to the NCO over the last 18 seconds of the FLL mode, and are handed off to the PLL as the set of initial conditions on f, df/dt.

The PLL requires accurate estimates f, df/dt to reliably acquire the signal. A separate estimator driven by the FLL is used to provide these estimates, since the FLL and PLL are contiguous and non-overlapping modes. Based upon considerations of performance, risk, and microprocessor loading, the LSE was used to implement the estimator.

As illustrated in FIG. 17, the LSE straight-line curve fit to the NCO input data generates the estimates f, df/dt at the end of the estimation interval. This process is illustrated in the timeline of FIG. 9. This timeline commences at time 0, when the FLL is started. At time t=4 seconds, ambiguity resolution (AR) commences. At time t=6 seconds, the LSE estimator commences operation and accumulates NCO input f estimates f₁, f₂ . . . f₂₅₆ at 18 symbol intervals until t=24 seconds, at which time FLL operation ceases.

The NCO input data f₁, f₂ . . . f₂₅₆ is accumulated to form values F and G in accordance with Equations 21 and 22: ##EQU12##

LSE coefficients are formed as shown in Table II, which shows both the theoretical coefficient relationships and the relationships actally used in the microprocessor.

                  TABLE II                                                         ______________________________________                                         Coefficient  Theory          Processor                                         ______________________________________                                         C.sub.1      2(N - 2)/N(N + 1)                                                                              -2/N                                              C.sub.2      6/N(N + 1)      6/N.sup.2                                         C.sub.3      -6/N(n + 1)T.sub.s                                                                             -6/N.sup.2 T.sub.s                                C.sub.4      12/N(N.sup.2 - 1)T.sub.s                                                                       12/N.sup.3 T.sub.s                                ______________________________________                                    

where

N=256 NCO samples

T_(s) =18/256 seconds=Time between NCO samples.

Using the coefficients shown in Table II, a novel set of relationships, described in Equations 23 and 24, is developed for calculating the f and df/dt estimates:

    f=f.sub.1 +C.sub.1 F+C.sub.2 G                             (14)

    df/dt=C.sub.3 F+C.sub.4 G                                  (15)

These algorithm represent a novel, powerful LSE method for determining the f, df/dt values.

PLL Operation

Once FLL operation has been completed, the receiver mode control system shifts receiver operation to the PLL mode.

The PLL mode may be modelled by the circuit shown in FIG. 16. The phase θ of the signal is provided to phase detector 650, whose output is a value φ. The phase discriminant φ is determined by estimator 655 from φ and is filtered by loop filter 660, which has a Laplace transform characteristic G(1+A/s+B/s²). The output of filter 660 is "X", which controls NCO 665, with a Laplace transform characteristic 665. The NCO output θ is provided to phase detector 650.

The one step recursive equations used to calculate the loop filtering for each symbol input φ from the PLL discriminant are described by the following relationships.

Loop filtering:

GB/s²

    X1=X1+G·B·T·φ

    X2=X2+T·X1

GA/s:

    X3=X3+G·A·T·φ

    X=G·φ+X3+X2

For loop initialization, the integration constants are the initial values for X1, X2, X3. These values are selected to cause the NCO to follow the LSE estimated f and df/dt at PLL startup until the PLL has time to modify their estimates. This specifies the integration constants to be

X1=df/dt

X2=0

X3=f

at PLL startup. There is a choice in either setting X2=0, X3=f or equivalently setting X2=f, X3=0. The loop coefficients or parameters G, A, B are calculated for each symbol as described below.

This PLL mode implements several novel features which substantially enhance the acquisition performance of the PLL mode. These novel features include the control of the PLL performance parameters B_(L), ξ₁, ξ₂ by a lock detector statistic ψ₂, and the use of an amplitude estimate A to normalize the phase discriminant which drives the loop.

The PLL function is updated at the symbol rate of 256 times per second. The PLL uses only the DFT filter centered around the signal, C₂, in its processing. The DFT filter is formed over the full symbol time. The PLL discriminant is input to the PLL loop filter which provides the feedback to track the signal coherently in phase.

The PLL is a third-order loop necessary to track the quadratic change in phase due to the strong Doppler rate present on the carrier frequency. The loop performance parameters B_(L), ξ₁, ξ₂ are a function of both time and the value of the PLL lock statistic ψ₂. ξ₁ and ξ₂ respectively correspond to the third-order real pole and the second-order complex pole pair of the closed loop transfer function.

During acquisition, an adaptive bandwidth control, based upon the lock statistic, narrows down the bandwidth as the PLL locks on the signal, to a final value given by the system bandwidth curve. Once phase lock is achieved, the bandwidth control passes over entirely to the system bandwidth decay curve, which decays linearly from 12 to 8 Hz over the 160 seconds following the start of the PLL module. The damping coefficients ξ₁, ξ₂, of the loop are fixed at 1.5 and 0.5.

A novel feature of the PLL mode is that the loop parameters B_(L), ξ₁, ξ₂ are independently controlled by the lock detector statistic ψ₂, in contrast to conventional PLL systems which only allow ψ₂ to control one of the three independent design parameters G, A, B. This novel feature results in a significant improvement in acquisition performance.

This feature may be better understood by considering known analog PLL loop applications of the lock detector statistic ψ₂. The loop gain G for analog Costas loops is the product of a hardware gain K and the signal amplitude A, so that G=K*A. As the C/N_(o) (carrier power to noise density ratio) drops, the loop gain C drops through the decrease in A since C=A² /2. This causes the (one-sided) loop noise bandwidth B_(L) to decrease and thereby partially alleviate the increase in loop jitter with C/N_(o) decrease. In addition, the K can be further reduced by controlling it with ψ₂.

Another application of ψ₂ control has been initial acquisition where, under low C/N_(o) conditions, it is desirable to open up B_(L) to allow "cycle slipping" to occur. As lockup takes place, the cycle slipping will gradually stop whereupon the B_(L) should be at a somewhat smaller value. Controlling this B_(L) decrease through variations in K as a function ψ₂ has proven to be effective.

From a control theoretic viewpoint, a complete state controller statistic or cost function should be an independent function of the PLL offset or mean and the 1-sigma jitter. While ψ₂ is a composite function of the mean and 1-sigma jitter, and therefore not a complete statistic, it is, nevertheless used as the acquisition controller in the preferred embodiment.

The PLL acquisition parameters G, A, B are controlled by using the PLL control law relationships in Equation 25. ##EQU13##

This functional form for the control law applies to the respective PLL acquisition parameters G, A, B upon replacing the dummy parameter X by G, A, B in turn.

The quadratic (second-order) relationship of X on the lock statistic was used instead of a linear (first-order) or a step function of ψ₂ to improve the phaselock acquisition performance.

The initial PLL parameters are the following:

Performance:

B_(L) =38.8 Hz

ξ1=0.002

ξ2=2.75

Processor:

G₀ =150.0

A₀ =5.02

B₀ -0.24

The final PLL parameters are the following:

Performance:

B_(L) =5 Hz

ξ1=1.5

ξ2=0.5

Processor:

G₁ =14.545

A₁ =4.848

B₁ =7.836

The initial values for G, A, B were obtained by selecting appropriate performance parameters for the frequency lock loop (FLL) or cycle slip mode of the PLL.

The final values for G, A, G listed were determined by selecting the appropriate B_(L), ξ1, ξ2, which are the final values listed.

The selection of the initial values for G, A B follows from consideration of the FLL or cycle slip operation carried out within the PLL mode. This FLL type operation is required to track out the extremes of the frequency and frequency rate errors from the FLL handover, which can occur at low C/N_(o). It is well known that FLL type operation of a PLL requires a PLL cycle slip and/or an FLL aided PLL. A PLL cycle slip operation has been implemented in the preferred embodiment. In the cycle slip mode, the PLL of the preferred embodiment behaves like a second-order FLL modelled as shown in FIG. 10, where T represents the symbol loop delay. In the phase track mode, the PLL behaves like the phase lock loop modelled as shown in FIG. 16.

The acquisition mode consists of a transition from the PLL cycle slip mode to the PLL phase track mode. During this transition, the PLL lock detector statistic ψ₂ (defined below) will increase in value as phase lock occurs and will simultaneously control the parameter G, A, B transitioning from the cycle slip values to the phase track values.

FIGS. 16 and 10 describe the PLL loop model in the phase track (phase lock), cycle slip modes respectively. In FIG. 10, the loop design parameters comprise B_(L), ξ and B/A. In this mode, the PLL develops a frequency estimate Δf. As the signal is acquired, i.e., as phase lock occurs, the PLL operation transitions to the phase track mode. In this mode, illustrated in FIG. 16, the PLL loop design parameters comprise B_(L), ξ1, ξ2.

Normalization of the PLL lock statistic ψ₂ and phase discriminant φ by the amplitude estimate A is an important factor in providing high predictable PLL performance. The PLL lock statistic ψ₂ in normalized form is defined by Equation 25: ##EQU14## where

    (I.sup.2 -Q.sup.2)=(Re C.sub.4).sup.2 -(Im C.sub.4).sup.2

C₄ =8-Point DFT tracking/detection filter =C₂ (1)-C₂ (2)

C₂ (K)=4-Point DFT tracking filter over K=1,2=first, second half-bits or Manchester bits

λ_(PLL) =0.5, lock detector threshold

<|C₂ |>=A

The PLL phase discriminant φ in normalized form is defined by Equation 26. ##EQU15## where I, Q are as defined with respect to Equation 25 and the η1, η2 are PLL loop scaling constants.

For PLL operation, the SLL feedback estimate t is quantized to T/16 increments. The SLL operation is changed at PLL startup to minimize the interaction between these two loops. During FLL operation, phase coherency between contiguous symbols is not required for any of the functions so the SLL loop was closed with the timing quantization or granularity equal to T/32 which is the A/D digitization interval. During PLL, the SLL timing estimate t determines the start time for the tracking/detection filter C₄ DFT summation. Changes in t between contiguous symbols cause phase shifts in C₄ which must be compensated to avoid SLL phase noise injection into the PLL. To keep this phase compensation in 90° increments so they can be implemented with add-only algebraic operations, the SLL t is restricted to T/16 jumps. Software realization of the t is a pointer that specifies the C₄ start time in the A/D output buffer memory. Thus, N_(SLL) is the SLL timing estimate t address or pointer for the DFT samples from the A/D memory. The PLL pointer N_(PLL) (K) is determined by the following relationship:

    N.sub.PLL (K)=N.sub.PLL (K-1)+2*|(N.sub.PLL (K-1)-N.sub.SLL (K-1))/2]

where the indices K, K-1 refer to symbols K, K-1 respectively, the address pointers are integers whose values are scaled to the A/D timing interval T/32, and the symbol |(o)| is the rounded down integer value of (o).

The PLL angle correction is -Q, I for a pointer change between symbols K-1 and K equal to N_(PLL) (K)-N_(PLL) (K-1)=-T/16, and +Q, -I for +T/16, where the pointer N_(PLL) is controlled by the SLL timing estimate and specifies the start time for the DFT filter summation.

Lock Detection

Another novel feature of the receiver comprises the implementation of a lock detector system to cover the complete 2 kHz I.F. bandwidth seen by the loops.

Insofar as is known to Applicant, there is no prior art for determining a lock detector to cover the complete Δf, Δt range over a wide variation in C/N_(o) conditions.

The primary disadvantage in using Manchester encoded BPSK modulation to achieve maximum E_(b) /N_(o) performance is the danger of "cycle slip," and the concurrent danger the receiver could track at a false lock point, i.e., any frequency Δf and time offset Δt different from zero at which the PLL will continue to operate. Cycle slip occurs when the combination of PLL loop stress and noise statistics cause the receiver to track at 180° from its nominal reference, thereby causing a sign inversion of all subsequent demodulated data. Cycle slip may also result in a bit slip or loss of a bit. In either case, the real danger of cycle slips is the possibility for the receiver to jump to a false lock point. In addition, during the acquisition process, a possibility exists for tracking a false lock point in handover to the PLL, which then continues to track at this false lock point.

The lock detector system of the preferred embodiment solves the false lock problem, and requires simultaneous confirmation of lock by the following six tests:

TEST 1:

ψ₂ ≧0.5 (This is to test for PLL phase lock near Δf=0 and Δt=0, where the PLL lock statistic ψ₂ is defined above in Equation 25.)

Tests 2-6 require reference to the graph of FIG. 11, which shows the locations of ten 4-point DFT filter energy accumulations in relation to time t and the 2 kHz IF frequency bandwidth. The following notations are utilized in tests 2-6:

ψC1=Energy accumulation of filter C1 at Δt=0

ψC2=Energy accumulation of filter C2 at Δt=0

ψC3=Energy accumulation of filter C3 at Δt=0

Max ψ=Maximum of the ψ's excluding ψC2

Min ψ=Minimum of the ψ's excluding ψC2

Max ψ1,3=Maximum of ψC1, ψC3

TEST 2:

ψC2/Min ψ>1.1 (This is a test to determine if C/N_(o) >21 db-Hz.)

TEST 3:

ψC2/Max ψ1,3>1.1

TEST 4:

ψC2/Max ψ>1.0 (Tests 3 and 4 are checks for large Δf, Δt offsets, with the threshold 1.1 set for C/No=21 db-Hz.)

TEST 5:

Min ψ/Max ψ1,3>0.9. (This test is a check to be sure that DFT filters C₁ and C₃ at Δt=0 only contain noise.)

TEST 6:

ψAR≧188 <|C₂ |>(This is an ambiguity resolver (AR) test which checks for Δt. Δf near T/2,0, with the AR test statistic ψAR defined as described below.)

During the PLL mode, the AR accumulates measurements of the "mid-bit" versus "bit" transitioning and compares the sum with "+" threshold to decide whether the SLL is correctly aligned or one-half bit off (which means it is tracking the mid-bit transitions) using the algorithm of Equation 27

    ψAR=C1(K)-C2(K)                                        (27)

where K is a value corresponding to an eight second accumulation.

The phase lock test (Test 1) is repeated every 1/4 second once phase lock has occurred. The remaining tests 2-6 are repeated every eight seconds after PLL startup, since these tests require about eight seconds to average out the noise variation of the coefficients used in the tests and it will be an abnormal occurrence for the the FLL, SLL and AR detectors to go out of lock once the signal has been acquired. Loss of phase lock has a much higher probability of occurrence, accounting for its more frequent lock checks.

Ambiguity Resolution during FLL/SLL

The ambiguity resolver (AR) works by establishing the true symbol edge of the Manchester encoded data versus the mid-symbol transition. Once established, two chances are then given for decision verification during the FLL operation.

With Manchester encoding, the symbol will always have a phase transition at the mid-symbol point and may or may not have a phase transition at the symbol edge depending upon the data stream. A counter is used as an integrator to determine the correct resolution. This integrator (or ambiguity statistic) counts up when a phase transition occurs at the assumed mid-symbol point and counts down when a phase transition occurs at the assumed symbol edge. This statistic is left to integrate continuously for a maximum period of six seconds or until it exceeds either the positive or negative AR threshold. The statistic is checked against the thresholds once per second by the mode control system.

If the positive threshold is exceeded, more phase transitions were detected at the assumed mid-symbol position than at the symbol edge so that the assumed Manchester symbol phasing was correct. In this case, the timing reference is left unchanged. If the negative threshold is exceeded, the opposite is true in that more phase transitions were detected at the assumed symbol edge than at the mid-symbol point. This implies that the assumed Manchester symbol phasing was a half symbol off, so the read-out pointer is moved by T/2 to align the symbol timing.

After AR lock is indicated, the AR is given two chances (six seconds maximum for each chance) to verify the original decision. If resolution is not established after the first six seconds or not verified consequentially, the receiver is returned to the scan mode or SPRT operation.

After four seconds into the FLL mode, the transients due to the initial offsets Δf, Δt will have settled down sufficiently to allow the AR to be turned on. Within roughly to seconds, the AR will have decided whether the SLL is tracking the mid-bit or bit transition points of the symbol. After the AR makes its decision, the discriminant changes are: (1) the FLL discriminant is switched from two half symbol DFT's to a full symbol IQ discriminant, and (2) the single mid-bit 4-point DFT is substituted for the two 3-point DFTs straddling the mid-bit and bit transition points. Within two additional six second trial periods, a confirming AR decision is required to reduce the false alarm of false decision probability.

The AR accumulates measurements of the mid-bit versus bit transitioning and compares the sum with +/- thresholds to decide whether the SLL is correctly aligned or one-half bit off (which means it is tracking the mid-bit transitions). The following notations are utilized for the AR test:

Threshold Testing ##EQU16## where: I_(K) (C_(uv) (M)=Indicator decisioning function of the detection filter C_(uv) (M) for symbol K.

C_(uv) (M)=Transition detection filter for M=1,2 and uv=up, dn.

Transition Counters C1, C2:

For M=1,2 ##EQU17##

These notations may be understood by reference to FIG. 14a-f. FIG. 14a illustrates encoded Manchester data symbols "1" and "0" as a function of time. In FIG. 14b, the tracking filters C₂ (1), C₂ (2), C₂ (3) are shown formed over three consecutive Manchester bits. FIGS. 14c-f illustrate and define the four transition detection filters C_(up) (1), C_(dn) (1), C_(up) (2), C_(dn) (2).

The AR test uses the relationship described in Equation 28.

    -λ.sub.c <C1(K+1)-(C2(K+1)>λ.sub.c           (28)

where C1(K+1)-C2(K+1)=ψAR defined in Equation 27, and λ_(c) =counter threshold.

If ψ_(AR) >λ_(c), then the decision is that AR is valid and the SLL is tracking the bit transition. If ψ_(AR) <-λ_(c), then the decision is that AR is valid, and the SLL is tracking the mid-bit transition. Otherwise, the result of the test is that there is no AR decision, and the AR test will be continued if there is not mode timeout.

The AR parameters that implement this AR relationship are the detection filter threshold and the counter threshold λ_(c).

The AR detection filter threshold λ is a function of the C/N_(o) and the bit transition rule. In the preferred embodiment, λ=√2<|C₂ |> was selected. The counter threshold value λ_(c) =50 was selected, and provides adequate AR times with low false alarm rates at low bit transition rates (BTR).

AR During PLL Mode

During the PLL mode, the AR operates as a lock detector and differs from the AR operation of the FLL/SLL mode only in the decision rule. The same AR decisioning statistic ψ_(AR) is used as in the FLL/SLL mode. One difference in the decision rule is that the ψ_(AR) is accumulated over an eight second period before an AR test is made of the lock detector tests, which means that (K+1) equals (8 seconds)×(256 symbols/second) equals 2048 when the test is made. Another difference in the decision rule is that ψ_(AR) is only compared to the positive threshold 188*<|C₂ |> to decide if the AR is still "in lock," i.e., still tracking the mid-bit transitions. The threshold constant 188 is considerably larger than the value 50 used during the FLL/SLL mode, because of the longer accumulation time for ψ_(AR), and the desire to have a very low probability of false alarm (P_(f)) or false indication of "in lock" status. In the PLL mode, an "out-of-lock" decision must be confirmed by the next eight second AR test to be considered valid, whereas in the FLL/SLL mode, two chances are provided to confirm the AR decision.

Receiver Mode Control

Referring to FIG. 12a, a detailed diagram of the mode control operation of the receiver is illustrated. At starting point 500, the receiver starts its operation. At step 505, flag BF is set to the value 1, and the mode control timer T_(BF) is set to 0.

At step 510, the SPRT mode is entered. The SPRT timer T is set to 0, the estimates of the signal frequency f and frequency rate f are set to their nominal values. The out-of-band noise energy estimate N is calculated for an eight second integration period, and used to initialize the one step recursive average. The handover counter HF is set to 0.

At step 515, the next SPRT sweep occurs through the frequency uncertainty range. The mode control timer t_(BF) is incremented, the DFT filters are formed and the energy accumulations are calculated using the present N value. At step 520, the threshold test described above occurs, and if no signal is deemed present, then the N value is updated, and the mode control proceeds to step 525, where the SPRT timer t is checked to determine if it has exceeded five minutes. If not, step 515 is repeated for another SPRT sweep. If at step 525, the SPRT timer value exceeds five minutes, then it is deemed necessary to obtain another estimate of the out-of-band energy N and thus the mode control proceeds to step 530.

At step 530, the mode control timer t_(BF) is tested to determine whether its value is greater than or equal to ten minutes. If so, then the mode control proceeds back to step 505 to reinitialize the timer. It t_(BF) is less than ten minutes, then the program enters SPRT routine at step 510.

If the SPRT threshold test indictes at step 520 that the signal is present within the uncertainty region, then at step 535 the handover timer t_(HF) is set to zero. At step 540, the mode control timer t_(BF) and the handover timer t_(HF) are incremented, and the handover counter HF is incremented.

At step 545, the Neyman-Pierson test (NP test) is performed as a check to determine whether a false alarm has been given by the SPRT that a signal is present. If the NP test indicates that no signal is found, then the mode control proceeds to step 548 where the value of the handover flag HF is checked if its value is greater than or equal to 2. If not, then the mode control goes to step 525, and thence either to step 515 or 530. If the value of the handover flag HF is greater than or equal to 2, then step 530 is entered.

If the NP test indicates the signal has been found, then the FLL/SLL is entered at step 550. The FLL/SLL timer is set to zero, and the FLL/SLL integration registers are set to zero. Also, in this step the ambiguity resolution (AR) integrators are set to zero, flag IAR is set to zero, as are AR counter N_(AR) and timer t_(AR).

Referring now to FIG. 12b at step 555, the next symbol is processed during the FLL/SLL, and the mode control timer t_(BF), the handover timer t_(HF) and the FLL/SLL loop timer t are incremented. At step 560, the FLL/SLL timer t is tested to determine whether its value is greater than or equal to four seconds. If not, then the mode control loops back to step 555. If the timer value is greater than or equal four seconds, then at step 562, the FLL/SLL loop timer t is checked to determine whether it is greater than or equal to six seconds. If not, step 565 is bypassed. If "yes," then at step 565, the estimated values for frequency f and rate of frequency change f are updated. At step 570, a decision is made to determine whether the flag IAR equals zero. This flag indicates the state of the FLL/SLL lock detectors, i.e., whether the FLL/SLL are "in lock" or "out-of-lock." If the state of IAR equals zero, then at step 575, and at step 580 the FLL/SLL timer t is checked to determine whether its value is greater than or equal to five seconds. If so, then the ambiguity resolution check routine is entered at step 585.

At step 585, the value of λ_(AR) is set to 50 for acquisition. At step 590, the ambiguity resolution timer t_(AR) is checked to determine whether its value is greater to or equal to six seconds. If it is not, then at step 600 a decision occurs to determine whether ambiguity has been resolved. If not, then the mode control continues to 635. If at step 600 the ambiguity has been resolved, then at step 605 the ambiguity resolution counter N_(AR) is incremented by 1, timer t_(AR) is set to zero and reset, the DFT operation is switched from 3-point DFT to 4-point DFT filter operation, and the discriminant for the determination of Δf is changed to the IQ discriminant for N_(R) equals 1. At step 615, a decision is made to determine whether the N_(AR) counter equals 1, indicating that ambiguity resolution has occurred. If N_(AR) is 1, then the mode control proceeds to step 635. If the N_(AR) counter does not equal 1, then at step 620 the ambiguity resolution is verified. If the result of the test is negative, then the mode control goes to step 630. At step 630, the value of counter N_(AR) is checked for equality to 3, indicating that ambiguity resolution has occurred and has not been verified after two attempts. If N_(AR) =3, then mode control branches to D shown in FIG. 12a. If the verification is positive at step 620, then at step 625 the value of IAR is set to 1, and the value for λ_(AR) is set to 189.

At step 635, the FLL/SLL timer t is checked to determine whether its value is greater than or equal to 24 seconds. If not, then the mode control reverts to step 555. If the timer is greater than or equal to 24 seconds, then the FLL/SLL mode is exited and the mode control proceeds to FIG. 13c.

At step 640, the estimates for f and f are calculated. At the end to step 645, a decision is made to determine whether the flag BF is equal to 1, indicating that the receiver operation has proceeded through the SPRT, FLL/SLL and handover. If BF=1, then at step 650 the mode control timer t_(BF) is set to 24 seconds and program control proceeds to step 655. If at step 645 the flag BF does not equal zero, then step 655 follows immediately.

At step 655, the phase-lock loop (PLL) is entered. During this step, the value N is scaled from a power to an amplitude basis, the PLL timer is set to 0. Flag PF and BF are set to 0. The demodulation operation commences also, although the data is not valid. All lock detectors states are set to 0, except the PLL lock detector. At step 660, which can also be entered via "B," the phase-lock loop is initialized by selection of the final acquisition noise bandwidth B_(L), and the control of the bandwidth by the ψ₂ factor is commenced. Flag VDF is set to 0. The PLL timer t is set to 0, as are the PL loop integrators and lock-detector states.

At step 665, the next symbol is processed by the phase-lock loop. The bandwidth B_(L) is updated; valid data is demodulated and output; and the lock-detector calculation is updated. At step 670, a decision is made to determine whether the phase-lock loop timer t is equal n/4 seconds where n is an integer. At every 1/4 second interval, that is, every 64th symbol, a lock-detector test is performed. If the result of the decision is negative, then receiver operation reverts to step 665 to process the next symbol. If the result of decision point 670 is positive, indicating that a lock-detector test should be performed, then at step 675 the values for the mode control clock t_(BF) and the handover clock t_(HF) are incremented. At step 680, the value of the handover clock t_(HF) is tested to determine whether it is greater than or equal to 11/2 minutes. If it is, then at step 685 the handover counter HF is set to 1, and the handover clock t_(HF) is set to 0. Receiver operation then proceeds to step 690 shown in FIG. 13d.

Step 690 comprises a decision point to determine whether the phase-lock timer t=n·8 seconds where n is an integer. The purpose of this test follows from the fact that every eight seconds, all of the lock-detectors, are checked. If t does not equal n·8, then at step 692 a test is performed to determine whether the value of flag VDF equals 1. If not, then the program proceeds to step E (FIG. 13e) indicating the PLL is still in the acquisition mode. If VDF=1, then the receiver operation proceeds to step 750 to test the PLL lock status.

If at step 690 t=n·8, then operation proceeds to step 695 which is to set the status of te lock-detectors. Step 700-720 implement the lock-detector tests 2-5 described hereinabove. Step 700 comprises a decision to determine whether the FLL/SLL test statistic is greater than or equal to λ₁. If not, then at state 705 the FLL/SLL state is checked to determine whether it equals 2. If it does, then at step 720 this state is set equal to 3 and program control proceeds to step 725 indicating that the "loss-of-lock" has been verified by the next eight second test. If the FLL/SLL state does not equal 2 at step 705, then at step 715 it is set equal to 2. If at step 710 the FLL/SLL test statistic does exceed λ₁, the FLL/SLL state is set equal to 1, and program control proceeds to step 725.

At steps 725-745, lock-detector test number 6 is implemented as described hereinabove. At step 725, the ambiguity resolution discriminant is checked to determine whether it is greater than λ₃. If it is not, then at step 30 the state of the ambiguity resolution is checked to determine it equals 2. If it does, then at step 745 the AR state is set equal to 3 and the program control proceeds to step 750. If the result of decision point 730 is negative, then AR state is set equal to 2 at step 740. Finally, if at step 725 the AR discriminant does exceed λ₃, then at step 735 the AR state is set equal to 1.

At steps 750-780, lock-detector test number 1 described hereinabove is implemented. At step 750, the PLL test statistic is checked to determine whether it is greater than λ₄. If not, then at step 755 the PLL state is checked to determine whether it equals 2. If so, then at step 770, t₂ is incremented and at step 755 it is checked to determine whether it equals or is greater than two seconds. If not, then receiver operation proceeds to step 785 at FIG. 13e. If t₂ is greater than or equal to two seconds, then at step 780 the PLL state is set equal to 3 and the operation proceeds to step 785. If at step 755 the PLL state does not equal 2, then at step 765 the PLL state is set to 2 and timer t₂ is set equal to 0. Finally, at step 760 if the PLL test statistic is greater than λ₄ at step 750, then at step 760 the PLL state is set equal to 1 and the timer t₂ is set equal to 0.

Referring now to FIG. 13e, at step 785, the states of all lock-detectors are checked to determine whether they each equal 1. If not, then the program proceeds to step 795; but if all lock-detector states equal 1, then at step 790 the values for the noise estimate N and frequency estimate f are updated.

At step 795, the FLL/SLL state is checked to determine whether it equals 3. If it does, then the operation proceeds to point "D" in FIG. 13a.

At step 815, the ambiguity resolution state is checked to determine whether it equals 3. If it does, then the operation proceeds to step 805. If not, the operation loops to step 820, which checks to determine whether the PLL state equals 3. If yes, then at step 825 the flag PF is checked to determine whether it is greater than or equal to 2. If yes, then the program proceeds to step 805, and if not, the program proceeds to B. At step 830, the timer t_(PF) is incremented and at step 835 its value is checked to determine whether it is greater than or equal to ten seconds. If it is, then at step 840 the flag PF is set equal 1 and timer PF is set equal to 0. At step 845, the mode control timer t_(BF) is checked to determine whether it is greater than or equal to three minutes. If it is, then at step 850 the timer is set equal to three minutes and the operation proceeds to step "A." If the result of decision point 845 is negative, then the operation does proceed also to point "A."

PLL acquisition indicated by mode "E," also described in FIG. 12, starts with step 855, incrementing timer t_(PF). At step 860, timer t_(PF) is checked to determine whether it is less than or equal to three seconds. If yes, then the receiver operation proceeds immediately to point "A." If no, then at step 865, timer t_(PF) is checked to determine whether it is less than or equal to eight seconds. If not, then at step 870 the flag HF is checked to determine whether it is greater than or equal to 2. If yes, then the program proceeds to routine "D," and if no, the operation proceeds to point "C." At step 875, the status of the PLL lock-detector is checked to determine whether PLL lock exists. If no, the operation proceeds to point "A." If the result of step 875 is positive, then at step 880 the PLL state is set equal to 1; the timer t_(PF) is set to 0; flag VDF is set to 1; and the bandwidth control is switched from being controlled by the factor ψ₂, to a time control. Finally, in step 880 the flag PF is incremented by integer 1.

The mode control system of the preferred embodiment is implemented within the digital processor of the receiver. The processor program which implements the controller follows the detailed flow chart described in FIG. 13, and includes the calculations described above with respect to the various modes of receiver operation. Since further details of the program per se form no part of the present invention and since the program may be implemented in many different ways as is well known to those skilled in the art, the actual program will not be described further. The actual programming details will be readily apparent to those skilled in the art.

It will be seen that the receiver employing the mode control system is sequenced through its various modes of operation in an efficient manner, and in the case of "loss-of-lock," the mode control system determines the appropriate restart point to minimize the signal reacquisition time. For example, the most typical out-of-lock condition will be loss of phase lock. In this event, it is generally not necessary to start at the beginning of the mode control operation, i.e., with the SPRT calculations, or even to repeat frequency and symbol timing acquisition.

There has been described in this application a novel receiver for acquiring and tracking a data communications signal which is at a frequency within a predetermined uncertainty frequency band. With the receiver of the preferred embodiment, acquisition occurs within a short time and the signal may be tracked even in the presence of severe link stresses.

It is understood that the above-described embodiments are merely illustrative of but a small number of the many possible specific embodiments which can represent applications of the principles of the present invention. Numerous and varied other arrangements can be readily devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the present invention. 

What is claimed is:
 1. In a communications receiver adapted to provide a coarse estimate of the frequency and symbol timing of a signal encoded with data symbols having a length T and having a frequency within a frequency uncertainty band, the improvement comprising:filter means including a filter which has a nominal bandwidth B Hz; means for centering the bandwidth of the filter means at said coarse frequency estimate; digitizer means coupled to the filter means for converting output signals from said filter means to a digital bit stream; digital processor means coupled to said digitizer means and said centering means for processing said digital bit stream in accordance with a predetermined sequence of program steps, said digital processor means comprising; matched digital filter means for dividing the bandwidth of said filter into a plurality of frequency sub-bands having a plurality of digital filters, each of the digital filters having a nominal bandwidth covering a respective one of said frequency sub-bands; symbol timing control means for controlling said matched digital filter meas, said control means providing a preselected timing offset for controlling each of the digital filters; means responsive to the matched digital filter means for detecting and accumulating values corresponding to the spectral energy within each frequency sub-band at preselected times dependent on said timing offset; means responsive to the detecting and accumulating means for selecting N contiguous sub-bands whose spectral energy values comprise a maximum first sum to form a first set of sub-bands; means for selecting the P<N contiguous sub-bands within said first set whose spectral energy values comprise a maximum second sum to form a second set of sub-bands; and means for selecting that sub-band within said second set having the largest energy accumulation value to form an improved coarse estimate of the signal frequency within said frequency uncertainty band said processor means providing said improved coarse estimate to said centering means.
 2. The improvement of claim 1 wherein said digital filter means comprises a plurality of frequency sub-bands of bandwidth 2/T, and centered at adjacent frequencies 1/T Hz apart.
 3. The improvement of claim 2 wherein said digital processor means further comprises to comprise means for determining an improved estimate of the symbol timing of said data symbols, said improved estimate comprising the timing offset at which said second set is found.
 4. The improvement of claim 3 wherein said digital processor means further comprises to comprise means for testing for the presence of said encoded signal received in accordance with said improved frequency and timing estimates.
 5. The improvement of claim 4 wherein said testing means comprises means for determining whether said largest energy accumulation value exceeds the product of a threshold constant λ and a noise power estimate N.
 6. A communications receiver employing a feedback loop to track a signal modulated with data symbols having a length T seconds, comprising:input filter means including a filter having a bandwidth B Hz for providing a filtered signal; analog-to-digital converter (A/D) means for converting the filtered signal from an analog signal to a digital signal, said A/D means operable to sample said analog signal and generate digital signals corresponding thereto at a sample rate R samples/second; and a digital processor coupled to said A/D means for processing said digital signals in accordance with a predetermined sequence of program steps, said digital processor comprising;(i) matched filter means for adaptively filtering said digital signals; said matched filter means including a bank of digital filters centered at frequencies separated by 1/T Hz and having a nominal bandwidth 1/T Hz, said matched filter means providing a signal value representative of the matched filter means output; and (ii) feedback loop means arranged to provide a feedback signal responsive to the matched filter means for tracking said signal value from the matched filter means, said feedback loop means including a discriminant means for adaptively determining a loop said said discriminant signal, a loop filter for filtering said discriminant signal in accordance with a predetermined filter characteristic, and a gain means for modifying the output of said loop filter by a gain factor G.
 7. The receiver of claim 6 wherein said discriminant means generates a first discriminant whose value Δf comprises the average of discriminant values Δf₁, Δf₂ over consecutive symbols, K, K+1, determined in accordance with a first relationship ##EQU18## where T represents the symbol length, C₂ represents the digital filter output centered at its respective frequency over the symbol K, C₁, C₃ represent the outputs of digital filters centered at frequencies 2/T Hz away from the center frequency of C₂ <> represents "estimate of" and C₁, C₃ represent the complex conjugate of C₁, C₃.
 8. The receiver of claim 7 where said discriminant means determines a new discriminant value for every two data symbols.
 9. The receiver of claim 6 wherein said discriminant means generates a discriminant whose value Δf is determined in accordance with the relationship. ##EQU19## where T is the symbol length, C₂ (1) represents the complex conjugate of the digital filter output value formed over the first half of the data symbol C₂ (2) represents the digital filter output value formed over the second half of the data symbol, the symbol <> represents "estimate of" and C₂ represents the digital filter output value formed over the entire data symbol.
 10. The receiver of claim 6 wherein said feedback loop means comprises a symbol lock loop (SLL) to synlchronize the matched filter means to the digital signal.
 11. The receiver of claim 10 wherein such signal modulation comprises Manchester coded binary phase shift keyed (BPSK) modulation wherein the Manchester bit rate is 1/2T Hz, and wherein said receiver further comprises ambiguity resolution (AR) means for determining whether the SLL is locked on a true symbol or mid-symbol Manchester bit transition.
 12. The receiver of claim 6 wherein said feedback loop means operates in first and second modes, said first mode comprising a frequency lock loop (FLL) mode and said second mode comprising a phase lock loop (PLL) mode.
 13. The receiver of claim 12 wherein said digital processor further comprises means for determining an estimate of the frequency of said modulated signal to initialize said PLL mode.
 14. The receiver of claim 13 wherein said estimating means determines a least squares estimate of said modulated signal frequency based upon said feedback signals generated by said feedback loop means during said FLL mode.
 15. The receiver of claim 6 wherein said feedback loop means comprises a phase lock loop (PLL).
 16. The receiver of claim 15 wherein said feedback loop means simultaneously and independently time controlling the PLL bandwidth B and damping factor.
 17. The receiver of claim 16 wherein said digital processor further adapted to comprises means for operating said PLL in a cycle slip mode and in a phase tracking mode.
 18. In a communications receiver employing a sequential probability ratio test (SPRT) to provide a coarse estimate of a frequency within a frequency uncertainty band of a signal modulated with data symbols, the improvement comprising:filter means including a filter which has a nominal bandwidth B Hz and frequency converting means for converting signals from said filter to converted output signals; digitizer means coupled to said filter means for digitizing the converted output signals from said filter means into a digital bit stream; a digital processor coupled to said digitizer means and said frequency converting means for processing said digital bit stream in accordance with a predetermined sequence of program steps, said digital processor comprising; matched digital filter means including a plurality M of digital filters dividing the bandwidth of said filter into a plurality of frequency regions each digital filter having a nominal bandwidth covering a respective one of said frequency regions; means for accumulating respective digital filter outputs over a time interval to provide spectral energy values representative of the received spectral energy within the respective frequency region covered by the respective digital filter; and means for storing said respective energy values and comparing such values against a predetermined threshold value to determine whether a signal has been found within each of the respective frequency regions, whereby said receiver provides a coarse estimate of the signal frequency within said frequency uncertainty band in the event one of such values exceeds said threshold value, said digital processor providing said coarse estimate to said frequency converting means.
 19. The receiver of claim 18 wherein said matched digital filter means comprises discrete Fourier Transform (DFT) filters, each centered at a predetermined location within said filter bandwidth.
 20. The receiver of claim 19 wherein each DFT filter has a nominal bandwidth D Hz, said predetermined locations are separated by D Hz, and the number M=B/D.
 21. The improvement of claim 18 wherein said storing and comparing means further comprises means for comparing said respective energy values against an adaptively determined noise threshold value to determine whether only noise is present within one of said frequency regions.
 22. The receiver of claim 21 wherein said digital processor comprises means for estimating the spectral noise energy level in the frequency regions.
 23. The receiver of claim 22 wherein each of said filters has a design point signal to noise ratio (SNR), and said means for accumulating the respective digital filter outputs is arranged to accumulate said energy values for each such region in accordance with the relationship

    ψ=Σ.sub.K (|C|.sup.2 -(1+α.sub.o /2)N)

where ψ represents the energy accumulation, where K indicates a summation over consecutive digital bits, |C| represents the energy present in the digital filters, α_(o) represents the design point SNR for the digital filter, N is a noise power estimate.
 24. The receiver of claim 23 wherein said digital processor further determines that no signal is present when ψ is less than .-λ_(A) N, where λ_(A) is a predetermined lower threshold value, and a signal is present when ψ is greater than λ_(B) N, where λ_(B) is a predetermined upper threshold value.
 25. The receiver, of claim 24 wherein said digital processor steps from a first frequency region to a second frequency region upon determining that no signal is provided by a first respective digital filter.
 26. The receiver of claim 24 wherein said digital processor steps from a first frequency region to a second frequency region upon elapsement of a predetermined dwell time.
 27. The improvement of claim 18 wherein said digital processor implements said digital matched filter means with discrete Fourier Transform (DFT) algorithms employing add-only operations.
 28. A communications receiver employing a feedback loop to acquire or track a signal modulated with data symbols, comprising:a filter means including a filter which has an output having the frequency within a bandwidth B Hz and means for converting signals at the filter output to converted output signals; digitizer means for converting signals from said filter means into a digital bit stream; a digital processor coupled to said digitizer means and said frequency converting means including a digital frequency lock loop (FLL), said digital processor processing said digital bit stream in accordance with a predetermined sequence of program steps and further including; matched filter means for adaptively filtering said digital bit stream to provide matched filter means output signals; FLL discriminant means responsive to the matched filter means for calculating an FLL discriminant signal; FLL digital loop filter means for filtering said discriminant signal to provide an FLL filter signal coupled to said frequency converting means; said digital processor simultaneously and independently time controlling the loop noise bandwidth B_(L) and the damping factor ξ.
 29. The receiver of claim 28 wherein said digital processor further comprises an FLL gain factor means for multiplying the FLL filter signal by a gain factor G, and wherein said digital processor provides said gain factor G and a loop filter constant A as a function of the loop noise bandwidth B_(L), the damping factor ξ and a loop scale constant η as follows:

    G=(1/η)(4B.sub.L /(1+1/4ξ.sup.2))

    A=B.sub.L /(ξ.sup.2 +1/4).


30. The improvement of claim 28 wherein said loop filter means is a second order filter, formed by first order recursive formulations of integrations.
 31. In a communication receiver, a method of determining a coarse estimate of the frequency of a data-symbol-modulated signal within a frequency uncertainty band, comprising a sequence of the following steps:(a) passing the received signal through an input filter having a bandwidth B Hz centered at a frequency window within the uncertainty band; (b) digitizing the filtered signal into a digital bit stream at a digitizer sample rate; (c) processing the digital bit stream in a plurality of matched digital filters whose collective bandwidths cover the bandwidth B of the input and provide respective filter outputs each representative of the spectral energy received in the bandwidth covered by the respective digital filter during each symbol period; (d) accumulating the respective filter outputs over a time interval to provide spectral energy values representative of the received spectral energy within the respective bandwidth of the respective digital filter; (e) storing the respective spectral energy values; (f) upon elapsement of said time interval, centering the bandwidth covered by said input frequency at a different frequency window within the frequency uncertainty band and repeating steps (b-e); (g) repeating step (f) until the entire frequency uncertainty band has been searched; (h) comparing the respective spectral energy values against a predetermined threshold value to determine whether a signal has been found within the bandwidth of particular digital filter within a particular frequency window; (i) coarse estimating a received signal frequency in response to said comparing step.
 32. The method of claim 31 wherein said processing step comprises:(i) employing a discrete Fourier transform (DFT) algorithm; (ii) implementing the DFT algorithm by coherently combining selected samples of said digital bit stream with add-only operations.
 33. The method of claim 31 further comprising:(i) if step (i) fails to provide a coarse estimate of the signal frequency, repeating steps (a)-(i), with the bandwidths of the respective digital filters of step (c) offset relative to the bandwidth of the input filter by a predetermined frequency offset.
 34. The method of claim 33 wherein said predetermined frequency offset is 1/2T, where T represents the period of the data symbols modulating the received signal.
 35. The method of claim 31 further comprising step:(j) coarse estimating the timing rate of the data symbols.
 36. The method of claim 35 further comprising:(k) if step (i) fails to provide a coarse estimate of the signal frequency, repeating steps (a)-(i) with the bandwidths of the respective digital filters of step (c) offset relative to the bandwidth of the input filter by predetermined frequency and time offsets.
 37. The method of claim 36 wherein said predetermined frequency offset is (1/2T) Hz, where T represents the symbol period, and said time offset is (1/8)T seconds. 